Respuesta :

Answer:

see explanation

Step-by-step explanation:

(1)

Corresponding angles are congruent, hence

∠W = ∠P = 80°

(2)

Ratios of corresponding sides are equal , that is

[tex]\frac{WZ}{PS}[/tex] = [tex]\frac{ZY}{RS}[/tex] = [tex]\frac{21}{7}[/tex] = 3

multiply both sides by 5

WZ = 5 × 3 = 15

(3)

Similarly

[tex]\frac{WX}{PQ}[/tex] = [tex]\frac{ZY}{RS}[/tex] = 3

[tex]\frac{WX}{7}[/tex] = 3 ( multiply both sides by 7 )

WX = 7 ×  3 = 21

(4)

The sides of WXYZ are each 3 times the size of PQRS

scale factor = 3





kudzordzifrancis
ANSWER

[tex]1. \: m< \: W=80 \degree[/tex]

[tex]2. WZ=15[/tex]

[tex]3. WX = 21[/tex]

[tex]4. \: k = 3[/tex]

EXPLANATION


Since WXYZ is a dilation of PQRS, the two shapes are similar.



The corresponding angles are equal.


Angle P corresponds to angle W.


This implies that,

[tex]m< \: W=m< \: P=80 \degree[/tex]



2. Side SR corresponds to ZY.

We can observe that,

[tex]|ZY|=21[/tex]



This implies that,


[tex]|ZY|=3 \times 7[/tex]


[tex]|ZY|=3|SR|[/tex]


This implies that,

[tex]WZ=3|SP|[/tex]


[tex]WZ=3 \times 5 = 15[/tex]


[tex]3. WX = 21[/tex]

This side, XZ is parallel to ZY. The opposite parallel sides of a parallelogram are equal.




4. The scale factor is

[tex] k= \frac{image \: length}{object \: length} [/tex]

[tex] k= \frac{21}{7} [/tex]



[tex] k= 3[/tex]


Therefore the scale factor is 3.

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